Some good book suggestions beyond linear algebra?

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High school student here...



Recently I was told I could go to the book store and pick out any math books I want. (2 or 3)



Does anyone have some good suggestions? I'm comfortable with anything involving calculus and I am currently studying linear algebra. It doesn't really even need to be a textbook just something that will help me learn and build mathematical maturity.




reference-request soft-question book-recommendation




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    Here's my answer to a closely related question: math.stackexchange.com/questions/1714966/…
    – Ethan Bolker
    6 hours ago














up vote
3
down vote

favorite
6












High school student here...



Recently I was told I could go to the book store and pick out any math books I want. (2 or 3)



Does anyone have some good suggestions? I'm comfortable with anything involving calculus and I am currently studying linear algebra. It doesn't really even need to be a textbook just something that will help me learn and build mathematical maturity.




reference-request soft-question book-recommendation




share|cite|improve this question

















  • 1




    Here's my answer to a closely related question: math.stackexchange.com/questions/1714966/…
    – Ethan Bolker
    6 hours ago












up vote
3
down vote

favorite
6









up vote
3
down vote

favorite
6






6





High school student here...



Recently I was told I could go to the book store and pick out any math books I want. (2 or 3)



Does anyone have some good suggestions? I'm comfortable with anything involving calculus and I am currently studying linear algebra. It doesn't really even need to be a textbook just something that will help me learn and build mathematical maturity.




reference-request soft-question book-recommendation




share|cite|improve this question













High school student here...



Recently I was told I could go to the book store and pick out any math books I want. (2 or 3)



Does anyone have some good suggestions? I'm comfortable with anything involving calculus and I am currently studying linear algebra. It doesn't really even need to be a textbook just something that will help me learn and build mathematical maturity.





reference-request soft-question book-recommendation





share|cite|improve this question












share|cite|improve this question




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edited 7 hours ago









José Carlos Santos

111k1695171




111k1695171









asked 7 hours ago









CaptainAmerica16

1466




1466







  • 1




    Here's my answer to a closely related question: math.stackexchange.com/questions/1714966/…
    – Ethan Bolker
    6 hours ago












  • 1




    Here's my answer to a closely related question: math.stackexchange.com/questions/1714966/…
    – Ethan Bolker
    6 hours ago







1




1




Here's my answer to a closely related question: math.stackexchange.com/questions/1714966/…
– Ethan Bolker
6 hours ago




Here's my answer to a closely related question: math.stackexchange.com/questions/1714966/…
– Ethan Bolker
6 hours ago










5 Answers
5






active

oldest

votes

















up vote
2
down vote



accepted










Have you seen What is Mathematics? by Courant and Robbins? It is by far the best introduction to mathematics that you can get your hands on, in my opinion. Here's a short form of the table of contents for your reference:



  1. Chapter I: The Natural Numbers

  2. Chapter II: The Number System of Mathematics

  3. Chapter III: Geometrical Constructions. The Algebra of Number Fields.

  4. Chapter IV: Projective Geometry. Axiomatics. Non-Euclidean Geometry.

  5. Chapter V: Topology

  6. Chapter VI: Functions and Limits

  7. Chapter VII: Maxima and Minima

  8. Chapter VIII: The Calculus

  9. Chapter IX: Recent Developments





share|cite|improve this answer





















  • Topology before calculus? This definitely seems worth checking out.
    – CaptainAmerica16
    7 hours ago











  • @CaptainAmerica16 Here are the subsections in the Topology chapter: 1. Euler's Formula for Polyhedra; 2. Topological Properties of Figures; 2.1 Topological Properties; 2.2 Connectivity; 3. Other Examples of Topological Theorems; 3.1 The Jordan Curve Theorem; 3.2 The Four Color Problem; 3.3 The Concept of Dimension; 3.4 A Fixed Point Theorem; 3.5 Knots; 4. The Topological Classification of Surfaces; 4.1 The Genus of a Surface; 4.2 The Euler Characteristic of a Surface; 4.3 One-Sided Surfaces
    – Brahadeesh
    7 hours ago










  • @CaptainAmerica16 The chapter ends with an appendix: 1. The Five Color Theorem; 2. The Jordan Curve Theorem for Polygons; 3. The Fundamental Theorem of Algebra.
    – Brahadeesh
    7 hours ago










  • @CaptainAmerica16 So, definitely a very interesting set of topics :)
    – Brahadeesh
    7 hours ago










  • It's official, this will be the first book I look for. Thanks!
    – CaptainAmerica16
    7 hours ago

















up vote
3
down vote













Two suggestions:




  • Discourses on Algebra, by Igor Shafarevich


  • Geometry: Euclid and Beyond, by Robin Hartshorne





share|cite|improve this answer





















  • +1 for Hartshorne's book. A very good suggestion.
    – Brahadeesh
    7 hours ago










  • @Brahadeesh Thank you.
    – José Carlos Santos
    7 hours ago










  • You like a lot Shafarevitch José...
    – Isham
    7 hours ago






  • 1




    @Isham I like the book Discourses on Algebra a lot.
    – José Carlos Santos
    7 hours ago










  • Everyone seems to really like these suggestions. I'll keep them in mind 😊
    – CaptainAmerica16
    7 hours ago

















up vote
2
down vote













If you wanna study linear algebra, then I'd like to suggest -
I) Linear Algebra (Friedberg, Insel, Spence)
II) Introduction to Linear Algebra (Gilbert Strang)
III) Linear Algebra (Kwak and Hong)
IV) Linear Algebra (Kenneth Hoffman, Ray Kunze)



For abstract algebra, go for -
I) A First Course in Abstract Algebra (J.B. Fraleigh)
II) Abstract Algebra (Dummit and Foote)
III) Contemporary Abstract Algebra (Joseph A. Gallian)



For Analysis, study -
I) Mathematical Analysis (Tom M. Apostol)
II) Real and Complex Analysis (Walter Rudin)
III) Real Analysis (Royden , Fitzpatrick)
IV) Introduction to Real Analysis (Bartle, Sherbert)






share|cite|improve this answer























  • Thank you! Abstract algebra is high on my list of further interests.
    – CaptainAmerica16
    7 hours ago










  • I'd say that Rudin requires quite a bit of mathematical maturity in the reader. I wouldn't recommend it to a high school student...
    – Brahadeesh
    7 hours ago










  • Then what should he study for analysis ?? @Brahadeesh
    – Anik Bhowmick
    6 hours ago










  • Perhaps Tao's Analysis I and II, or Sherbert and Bartle's Introduction to Real Analysis would be my recommendations. But Apostol is good too!
    – Brahadeesh
    6 hours ago










  • Yeah, thanks @Brahadeesh, I forgot to mention Bartle-Sherbert.
    – Anik Bhowmick
    6 hours ago

















up vote
1
down vote













V. Prasolov's Problems and Theorems in Linear Algebra will not only teach you everything you need to know about linear algebra, but also give you germs of ideas that will prove very useful later if you study more advanced mathematics where linear algebra occurs in a way or another.






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  • Wow, thank you so much for the link! This will be really helpful.
    – CaptainAmerica16
    7 hours ago

















up vote
1
down vote













Vector Analysis by Murray Spiegel is one good book with lots of exercises. Also I googled "Cambridge University Maths Reading List" and found this. I am sure others exist if you look.



I read Fraleigh's "First Course in Abstract Algebra" when I was at school, and found it accessible and good.



Körner's "Calculus for the ambitious" is a quirky approach - but geared to building understanding in the bridge between "calculus" at school and "analysis" at university.



And Feynman's Lectures on Physics are worth reading, too.






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  • +1 For the reading list. Thanks :)
    – CaptainAmerica16
    6 hours ago










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5 Answers
5






active

oldest

votes








5 Answers
5






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
2
down vote



accepted










Have you seen What is Mathematics? by Courant and Robbins? It is by far the best introduction to mathematics that you can get your hands on, in my opinion. Here's a short form of the table of contents for your reference:



  1. Chapter I: The Natural Numbers

  2. Chapter II: The Number System of Mathematics

  3. Chapter III: Geometrical Constructions. The Algebra of Number Fields.

  4. Chapter IV: Projective Geometry. Axiomatics. Non-Euclidean Geometry.

  5. Chapter V: Topology

  6. Chapter VI: Functions and Limits

  7. Chapter VII: Maxima and Minima

  8. Chapter VIII: The Calculus

  9. Chapter IX: Recent Developments





share|cite|improve this answer





















  • Topology before calculus? This definitely seems worth checking out.
    – CaptainAmerica16
    7 hours ago











  • @CaptainAmerica16 Here are the subsections in the Topology chapter: 1. Euler's Formula for Polyhedra; 2. Topological Properties of Figures; 2.1 Topological Properties; 2.2 Connectivity; 3. Other Examples of Topological Theorems; 3.1 The Jordan Curve Theorem; 3.2 The Four Color Problem; 3.3 The Concept of Dimension; 3.4 A Fixed Point Theorem; 3.5 Knots; 4. The Topological Classification of Surfaces; 4.1 The Genus of a Surface; 4.2 The Euler Characteristic of a Surface; 4.3 One-Sided Surfaces
    – Brahadeesh
    7 hours ago










  • @CaptainAmerica16 The chapter ends with an appendix: 1. The Five Color Theorem; 2. The Jordan Curve Theorem for Polygons; 3. The Fundamental Theorem of Algebra.
    – Brahadeesh
    7 hours ago










  • @CaptainAmerica16 So, definitely a very interesting set of topics :)
    – Brahadeesh
    7 hours ago










  • It's official, this will be the first book I look for. Thanks!
    – CaptainAmerica16
    7 hours ago














up vote
2
down vote



accepted










Have you seen What is Mathematics? by Courant and Robbins? It is by far the best introduction to mathematics that you can get your hands on, in my opinion. Here's a short form of the table of contents for your reference:



  1. Chapter I: The Natural Numbers

  2. Chapter II: The Number System of Mathematics

  3. Chapter III: Geometrical Constructions. The Algebra of Number Fields.

  4. Chapter IV: Projective Geometry. Axiomatics. Non-Euclidean Geometry.

  5. Chapter V: Topology

  6. Chapter VI: Functions and Limits

  7. Chapter VII: Maxima and Minima

  8. Chapter VIII: The Calculus

  9. Chapter IX: Recent Developments





share|cite|improve this answer





















  • Topology before calculus? This definitely seems worth checking out.
    – CaptainAmerica16
    7 hours ago











  • @CaptainAmerica16 Here are the subsections in the Topology chapter: 1. Euler's Formula for Polyhedra; 2. Topological Properties of Figures; 2.1 Topological Properties; 2.2 Connectivity; 3. Other Examples of Topological Theorems; 3.1 The Jordan Curve Theorem; 3.2 The Four Color Problem; 3.3 The Concept of Dimension; 3.4 A Fixed Point Theorem; 3.5 Knots; 4. The Topological Classification of Surfaces; 4.1 The Genus of a Surface; 4.2 The Euler Characteristic of a Surface; 4.3 One-Sided Surfaces
    – Brahadeesh
    7 hours ago










  • @CaptainAmerica16 The chapter ends with an appendix: 1. The Five Color Theorem; 2. The Jordan Curve Theorem for Polygons; 3. The Fundamental Theorem of Algebra.
    – Brahadeesh
    7 hours ago










  • @CaptainAmerica16 So, definitely a very interesting set of topics :)
    – Brahadeesh
    7 hours ago










  • It's official, this will be the first book I look for. Thanks!
    – CaptainAmerica16
    7 hours ago












up vote
2
down vote



accepted







up vote
2
down vote



accepted






Have you seen What is Mathematics? by Courant and Robbins? It is by far the best introduction to mathematics that you can get your hands on, in my opinion. Here's a short form of the table of contents for your reference:



  1. Chapter I: The Natural Numbers

  2. Chapter II: The Number System of Mathematics

  3. Chapter III: Geometrical Constructions. The Algebra of Number Fields.

  4. Chapter IV: Projective Geometry. Axiomatics. Non-Euclidean Geometry.

  5. Chapter V: Topology

  6. Chapter VI: Functions and Limits

  7. Chapter VII: Maxima and Minima

  8. Chapter VIII: The Calculus

  9. Chapter IX: Recent Developments





share|cite|improve this answer













Have you seen What is Mathematics? by Courant and Robbins? It is by far the best introduction to mathematics that you can get your hands on, in my opinion. Here's a short form of the table of contents for your reference:



  1. Chapter I: The Natural Numbers

  2. Chapter II: The Number System of Mathematics

  3. Chapter III: Geometrical Constructions. The Algebra of Number Fields.

  4. Chapter IV: Projective Geometry. Axiomatics. Non-Euclidean Geometry.

  5. Chapter V: Topology

  6. Chapter VI: Functions and Limits

  7. Chapter VII: Maxima and Minima

  8. Chapter VIII: The Calculus

  9. Chapter IX: Recent Developments






share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered 7 hours ago









Brahadeesh

3,19231143




3,19231143











  • Topology before calculus? This definitely seems worth checking out.
    – CaptainAmerica16
    7 hours ago











  • @CaptainAmerica16 Here are the subsections in the Topology chapter: 1. Euler's Formula for Polyhedra; 2. Topological Properties of Figures; 2.1 Topological Properties; 2.2 Connectivity; 3. Other Examples of Topological Theorems; 3.1 The Jordan Curve Theorem; 3.2 The Four Color Problem; 3.3 The Concept of Dimension; 3.4 A Fixed Point Theorem; 3.5 Knots; 4. The Topological Classification of Surfaces; 4.1 The Genus of a Surface; 4.2 The Euler Characteristic of a Surface; 4.3 One-Sided Surfaces
    – Brahadeesh
    7 hours ago










  • @CaptainAmerica16 The chapter ends with an appendix: 1. The Five Color Theorem; 2. The Jordan Curve Theorem for Polygons; 3. The Fundamental Theorem of Algebra.
    – Brahadeesh
    7 hours ago










  • @CaptainAmerica16 So, definitely a very interesting set of topics :)
    – Brahadeesh
    7 hours ago










  • It's official, this will be the first book I look for. Thanks!
    – CaptainAmerica16
    7 hours ago
















  • Topology before calculus? This definitely seems worth checking out.
    – CaptainAmerica16
    7 hours ago











  • @CaptainAmerica16 Here are the subsections in the Topology chapter: 1. Euler's Formula for Polyhedra; 2. Topological Properties of Figures; 2.1 Topological Properties; 2.2 Connectivity; 3. Other Examples of Topological Theorems; 3.1 The Jordan Curve Theorem; 3.2 The Four Color Problem; 3.3 The Concept of Dimension; 3.4 A Fixed Point Theorem; 3.5 Knots; 4. The Topological Classification of Surfaces; 4.1 The Genus of a Surface; 4.2 The Euler Characteristic of a Surface; 4.3 One-Sided Surfaces
    – Brahadeesh
    7 hours ago










  • @CaptainAmerica16 The chapter ends with an appendix: 1. The Five Color Theorem; 2. The Jordan Curve Theorem for Polygons; 3. The Fundamental Theorem of Algebra.
    – Brahadeesh
    7 hours ago










  • @CaptainAmerica16 So, definitely a very interesting set of topics :)
    – Brahadeesh
    7 hours ago










  • It's official, this will be the first book I look for. Thanks!
    – CaptainAmerica16
    7 hours ago















Topology before calculus? This definitely seems worth checking out.
– CaptainAmerica16
7 hours ago





Topology before calculus? This definitely seems worth checking out.
– CaptainAmerica16
7 hours ago













@CaptainAmerica16 Here are the subsections in the Topology chapter: 1. Euler's Formula for Polyhedra; 2. Topological Properties of Figures; 2.1 Topological Properties; 2.2 Connectivity; 3. Other Examples of Topological Theorems; 3.1 The Jordan Curve Theorem; 3.2 The Four Color Problem; 3.3 The Concept of Dimension; 3.4 A Fixed Point Theorem; 3.5 Knots; 4. The Topological Classification of Surfaces; 4.1 The Genus of a Surface; 4.2 The Euler Characteristic of a Surface; 4.3 One-Sided Surfaces
– Brahadeesh
7 hours ago




@CaptainAmerica16 Here are the subsections in the Topology chapter: 1. Euler's Formula for Polyhedra; 2. Topological Properties of Figures; 2.1 Topological Properties; 2.2 Connectivity; 3. Other Examples of Topological Theorems; 3.1 The Jordan Curve Theorem; 3.2 The Four Color Problem; 3.3 The Concept of Dimension; 3.4 A Fixed Point Theorem; 3.5 Knots; 4. The Topological Classification of Surfaces; 4.1 The Genus of a Surface; 4.2 The Euler Characteristic of a Surface; 4.3 One-Sided Surfaces
– Brahadeesh
7 hours ago












@CaptainAmerica16 The chapter ends with an appendix: 1. The Five Color Theorem; 2. The Jordan Curve Theorem for Polygons; 3. The Fundamental Theorem of Algebra.
– Brahadeesh
7 hours ago




@CaptainAmerica16 The chapter ends with an appendix: 1. The Five Color Theorem; 2. The Jordan Curve Theorem for Polygons; 3. The Fundamental Theorem of Algebra.
– Brahadeesh
7 hours ago












@CaptainAmerica16 So, definitely a very interesting set of topics :)
– Brahadeesh
7 hours ago




@CaptainAmerica16 So, definitely a very interesting set of topics :)
– Brahadeesh
7 hours ago












It's official, this will be the first book I look for. Thanks!
– CaptainAmerica16
7 hours ago




It's official, this will be the first book I look for. Thanks!
– CaptainAmerica16
7 hours ago










up vote
3
down vote













Two suggestions:




  • Discourses on Algebra, by Igor Shafarevich


  • Geometry: Euclid and Beyond, by Robin Hartshorne





share|cite|improve this answer





















  • +1 for Hartshorne's book. A very good suggestion.
    – Brahadeesh
    7 hours ago










  • @Brahadeesh Thank you.
    – José Carlos Santos
    7 hours ago










  • You like a lot Shafarevitch José...
    – Isham
    7 hours ago






  • 1




    @Isham I like the book Discourses on Algebra a lot.
    – José Carlos Santos
    7 hours ago










  • Everyone seems to really like these suggestions. I'll keep them in mind 😊
    – CaptainAmerica16
    7 hours ago














up vote
3
down vote













Two suggestions:




  • Discourses on Algebra, by Igor Shafarevich


  • Geometry: Euclid and Beyond, by Robin Hartshorne





share|cite|improve this answer





















  • +1 for Hartshorne's book. A very good suggestion.
    – Brahadeesh
    7 hours ago










  • @Brahadeesh Thank you.
    – José Carlos Santos
    7 hours ago










  • You like a lot Shafarevitch José...
    – Isham
    7 hours ago






  • 1




    @Isham I like the book Discourses on Algebra a lot.
    – José Carlos Santos
    7 hours ago










  • Everyone seems to really like these suggestions. I'll keep them in mind 😊
    – CaptainAmerica16
    7 hours ago












up vote
3
down vote










up vote
3
down vote









Two suggestions:




  • Discourses on Algebra, by Igor Shafarevich


  • Geometry: Euclid and Beyond, by Robin Hartshorne





share|cite|improve this answer













Two suggestions:




  • Discourses on Algebra, by Igor Shafarevich


  • Geometry: Euclid and Beyond, by Robin Hartshorne






share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered 7 hours ago









José Carlos Santos

111k1695171




111k1695171











  • +1 for Hartshorne's book. A very good suggestion.
    – Brahadeesh
    7 hours ago










  • @Brahadeesh Thank you.
    – José Carlos Santos
    7 hours ago










  • You like a lot Shafarevitch José...
    – Isham
    7 hours ago






  • 1




    @Isham I like the book Discourses on Algebra a lot.
    – José Carlos Santos
    7 hours ago










  • Everyone seems to really like these suggestions. I'll keep them in mind 😊
    – CaptainAmerica16
    7 hours ago
















  • +1 for Hartshorne's book. A very good suggestion.
    – Brahadeesh
    7 hours ago










  • @Brahadeesh Thank you.
    – José Carlos Santos
    7 hours ago










  • You like a lot Shafarevitch José...
    – Isham
    7 hours ago






  • 1




    @Isham I like the book Discourses on Algebra a lot.
    – José Carlos Santos
    7 hours ago










  • Everyone seems to really like these suggestions. I'll keep them in mind 😊
    – CaptainAmerica16
    7 hours ago















+1 for Hartshorne's book. A very good suggestion.
– Brahadeesh
7 hours ago




+1 for Hartshorne's book. A very good suggestion.
– Brahadeesh
7 hours ago












@Brahadeesh Thank you.
– José Carlos Santos
7 hours ago




@Brahadeesh Thank you.
– José Carlos Santos
7 hours ago












You like a lot Shafarevitch José...
– Isham
7 hours ago




You like a lot Shafarevitch José...
– Isham
7 hours ago




1




1




@Isham I like the book Discourses on Algebra a lot.
– José Carlos Santos
7 hours ago




@Isham I like the book Discourses on Algebra a lot.
– José Carlos Santos
7 hours ago












Everyone seems to really like these suggestions. I'll keep them in mind 😊
– CaptainAmerica16
7 hours ago




Everyone seems to really like these suggestions. I'll keep them in mind 😊
– CaptainAmerica16
7 hours ago










up vote
2
down vote













If you wanna study linear algebra, then I'd like to suggest -
I) Linear Algebra (Friedberg, Insel, Spence)
II) Introduction to Linear Algebra (Gilbert Strang)
III) Linear Algebra (Kwak and Hong)
IV) Linear Algebra (Kenneth Hoffman, Ray Kunze)



For abstract algebra, go for -
I) A First Course in Abstract Algebra (J.B. Fraleigh)
II) Abstract Algebra (Dummit and Foote)
III) Contemporary Abstract Algebra (Joseph A. Gallian)



For Analysis, study -
I) Mathematical Analysis (Tom M. Apostol)
II) Real and Complex Analysis (Walter Rudin)
III) Real Analysis (Royden , Fitzpatrick)
IV) Introduction to Real Analysis (Bartle, Sherbert)






share|cite|improve this answer























  • Thank you! Abstract algebra is high on my list of further interests.
    – CaptainAmerica16
    7 hours ago










  • I'd say that Rudin requires quite a bit of mathematical maturity in the reader. I wouldn't recommend it to a high school student...
    – Brahadeesh
    7 hours ago










  • Then what should he study for analysis ?? @Brahadeesh
    – Anik Bhowmick
    6 hours ago










  • Perhaps Tao's Analysis I and II, or Sherbert and Bartle's Introduction to Real Analysis would be my recommendations. But Apostol is good too!
    – Brahadeesh
    6 hours ago










  • Yeah, thanks @Brahadeesh, I forgot to mention Bartle-Sherbert.
    – Anik Bhowmick
    6 hours ago














up vote
2
down vote













If you wanna study linear algebra, then I'd like to suggest -
I) Linear Algebra (Friedberg, Insel, Spence)
II) Introduction to Linear Algebra (Gilbert Strang)
III) Linear Algebra (Kwak and Hong)
IV) Linear Algebra (Kenneth Hoffman, Ray Kunze)



For abstract algebra, go for -
I) A First Course in Abstract Algebra (J.B. Fraleigh)
II) Abstract Algebra (Dummit and Foote)
III) Contemporary Abstract Algebra (Joseph A. Gallian)



For Analysis, study -
I) Mathematical Analysis (Tom M. Apostol)
II) Real and Complex Analysis (Walter Rudin)
III) Real Analysis (Royden , Fitzpatrick)
IV) Introduction to Real Analysis (Bartle, Sherbert)






share|cite|improve this answer























  • Thank you! Abstract algebra is high on my list of further interests.
    – CaptainAmerica16
    7 hours ago










  • I'd say that Rudin requires quite a bit of mathematical maturity in the reader. I wouldn't recommend it to a high school student...
    – Brahadeesh
    7 hours ago










  • Then what should he study for analysis ?? @Brahadeesh
    – Anik Bhowmick
    6 hours ago










  • Perhaps Tao's Analysis I and II, or Sherbert and Bartle's Introduction to Real Analysis would be my recommendations. But Apostol is good too!
    – Brahadeesh
    6 hours ago










  • Yeah, thanks @Brahadeesh, I forgot to mention Bartle-Sherbert.
    – Anik Bhowmick
    6 hours ago












up vote
2
down vote










up vote
2
down vote









If you wanna study linear algebra, then I'd like to suggest -
I) Linear Algebra (Friedberg, Insel, Spence)
II) Introduction to Linear Algebra (Gilbert Strang)
III) Linear Algebra (Kwak and Hong)
IV) Linear Algebra (Kenneth Hoffman, Ray Kunze)



For abstract algebra, go for -
I) A First Course in Abstract Algebra (J.B. Fraleigh)
II) Abstract Algebra (Dummit and Foote)
III) Contemporary Abstract Algebra (Joseph A. Gallian)



For Analysis, study -
I) Mathematical Analysis (Tom M. Apostol)
II) Real and Complex Analysis (Walter Rudin)
III) Real Analysis (Royden , Fitzpatrick)
IV) Introduction to Real Analysis (Bartle, Sherbert)






share|cite|improve this answer















If you wanna study linear algebra, then I'd like to suggest -
I) Linear Algebra (Friedberg, Insel, Spence)
II) Introduction to Linear Algebra (Gilbert Strang)
III) Linear Algebra (Kwak and Hong)
IV) Linear Algebra (Kenneth Hoffman, Ray Kunze)



For abstract algebra, go for -
I) A First Course in Abstract Algebra (J.B. Fraleigh)
II) Abstract Algebra (Dummit and Foote)
III) Contemporary Abstract Algebra (Joseph A. Gallian)



For Analysis, study -
I) Mathematical Analysis (Tom M. Apostol)
II) Real and Complex Analysis (Walter Rudin)
III) Real Analysis (Royden , Fitzpatrick)
IV) Introduction to Real Analysis (Bartle, Sherbert)







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited 6 hours ago


























answered 7 hours ago









Anik Bhowmick

848




848











  • Thank you! Abstract algebra is high on my list of further interests.
    – CaptainAmerica16
    7 hours ago










  • I'd say that Rudin requires quite a bit of mathematical maturity in the reader. I wouldn't recommend it to a high school student...
    – Brahadeesh
    7 hours ago










  • Then what should he study for analysis ?? @Brahadeesh
    – Anik Bhowmick
    6 hours ago










  • Perhaps Tao's Analysis I and II, or Sherbert and Bartle's Introduction to Real Analysis would be my recommendations. But Apostol is good too!
    – Brahadeesh
    6 hours ago










  • Yeah, thanks @Brahadeesh, I forgot to mention Bartle-Sherbert.
    – Anik Bhowmick
    6 hours ago
















  • Thank you! Abstract algebra is high on my list of further interests.
    – CaptainAmerica16
    7 hours ago










  • I'd say that Rudin requires quite a bit of mathematical maturity in the reader. I wouldn't recommend it to a high school student...
    – Brahadeesh
    7 hours ago










  • Then what should he study for analysis ?? @Brahadeesh
    – Anik Bhowmick
    6 hours ago










  • Perhaps Tao's Analysis I and II, or Sherbert and Bartle's Introduction to Real Analysis would be my recommendations. But Apostol is good too!
    – Brahadeesh
    6 hours ago










  • Yeah, thanks @Brahadeesh, I forgot to mention Bartle-Sherbert.
    – Anik Bhowmick
    6 hours ago















Thank you! Abstract algebra is high on my list of further interests.
– CaptainAmerica16
7 hours ago




Thank you! Abstract algebra is high on my list of further interests.
– CaptainAmerica16
7 hours ago












I'd say that Rudin requires quite a bit of mathematical maturity in the reader. I wouldn't recommend it to a high school student...
– Brahadeesh
7 hours ago




I'd say that Rudin requires quite a bit of mathematical maturity in the reader. I wouldn't recommend it to a high school student...
– Brahadeesh
7 hours ago












Then what should he study for analysis ?? @Brahadeesh
– Anik Bhowmick
6 hours ago




Then what should he study for analysis ?? @Brahadeesh
– Anik Bhowmick
6 hours ago












Perhaps Tao's Analysis I and II, or Sherbert and Bartle's Introduction to Real Analysis would be my recommendations. But Apostol is good too!
– Brahadeesh
6 hours ago




Perhaps Tao's Analysis I and II, or Sherbert and Bartle's Introduction to Real Analysis would be my recommendations. But Apostol is good too!
– Brahadeesh
6 hours ago












Yeah, thanks @Brahadeesh, I forgot to mention Bartle-Sherbert.
– Anik Bhowmick
6 hours ago




Yeah, thanks @Brahadeesh, I forgot to mention Bartle-Sherbert.
– Anik Bhowmick
6 hours ago










up vote
1
down vote













V. Prasolov's Problems and Theorems in Linear Algebra will not only teach you everything you need to know about linear algebra, but also give you germs of ideas that will prove very useful later if you study more advanced mathematics where linear algebra occurs in a way or another.






share|cite|improve this answer





















  • Wow, thank you so much for the link! This will be really helpful.
    – CaptainAmerica16
    7 hours ago














up vote
1
down vote













V. Prasolov's Problems and Theorems in Linear Algebra will not only teach you everything you need to know about linear algebra, but also give you germs of ideas that will prove very useful later if you study more advanced mathematics where linear algebra occurs in a way or another.






share|cite|improve this answer





















  • Wow, thank you so much for the link! This will be really helpful.
    – CaptainAmerica16
    7 hours ago












up vote
1
down vote










up vote
1
down vote









V. Prasolov's Problems and Theorems in Linear Algebra will not only teach you everything you need to know about linear algebra, but also give you germs of ideas that will prove very useful later if you study more advanced mathematics where linear algebra occurs in a way or another.






share|cite|improve this answer













V. Prasolov's Problems and Theorems in Linear Algebra will not only teach you everything you need to know about linear algebra, but also give you germs of ideas that will prove very useful later if you study more advanced mathematics where linear algebra occurs in a way or another.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered 7 hours ago









Arnaud Mortier

17.6k21656




17.6k21656











  • Wow, thank you so much for the link! This will be really helpful.
    – CaptainAmerica16
    7 hours ago
















  • Wow, thank you so much for the link! This will be really helpful.
    – CaptainAmerica16
    7 hours ago















Wow, thank you so much for the link! This will be really helpful.
– CaptainAmerica16
7 hours ago




Wow, thank you so much for the link! This will be really helpful.
– CaptainAmerica16
7 hours ago










up vote
1
down vote













Vector Analysis by Murray Spiegel is one good book with lots of exercises. Also I googled "Cambridge University Maths Reading List" and found this. I am sure others exist if you look.



I read Fraleigh's "First Course in Abstract Algebra" when I was at school, and found it accessible and good.



Körner's "Calculus for the ambitious" is a quirky approach - but geared to building understanding in the bridge between "calculus" at school and "analysis" at university.



And Feynman's Lectures on Physics are worth reading, too.






share|cite|improve this answer





















  • +1 For the reading list. Thanks :)
    – CaptainAmerica16
    6 hours ago














up vote
1
down vote













Vector Analysis by Murray Spiegel is one good book with lots of exercises. Also I googled "Cambridge University Maths Reading List" and found this. I am sure others exist if you look.



I read Fraleigh's "First Course in Abstract Algebra" when I was at school, and found it accessible and good.



Körner's "Calculus for the ambitious" is a quirky approach - but geared to building understanding in the bridge between "calculus" at school and "analysis" at university.



And Feynman's Lectures on Physics are worth reading, too.






share|cite|improve this answer





















  • +1 For the reading list. Thanks :)
    – CaptainAmerica16
    6 hours ago












up vote
1
down vote










up vote
1
down vote









Vector Analysis by Murray Spiegel is one good book with lots of exercises. Also I googled "Cambridge University Maths Reading List" and found this. I am sure others exist if you look.



I read Fraleigh's "First Course in Abstract Algebra" when I was at school, and found it accessible and good.



Körner's "Calculus for the ambitious" is a quirky approach - but geared to building understanding in the bridge between "calculus" at school and "analysis" at university.



And Feynman's Lectures on Physics are worth reading, too.






share|cite|improve this answer













Vector Analysis by Murray Spiegel is one good book with lots of exercises. Also I googled "Cambridge University Maths Reading List" and found this. I am sure others exist if you look.



I read Fraleigh's "First Course in Abstract Algebra" when I was at school, and found it accessible and good.



Körner's "Calculus for the ambitious" is a quirky approach - but geared to building understanding in the bridge between "calculus" at school and "analysis" at university.



And Feynman's Lectures on Physics are worth reading, too.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered 6 hours ago









Mark Bennet

76.3k772169




76.3k772169











  • +1 For the reading list. Thanks :)
    – CaptainAmerica16
    6 hours ago
















  • +1 For the reading list. Thanks :)
    – CaptainAmerica16
    6 hours ago















+1 For the reading list. Thanks :)
– CaptainAmerica16
6 hours ago




+1 For the reading list. Thanks :)
– CaptainAmerica16
6 hours ago












 

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